Linear recursion relations for the instanton corrections to the effective prepotential are derived for N=2 supersymmetric gauge theories with one hypermultiplet in the adjoint representation of SU(N) using the Calogero-Moser parameterization of the Seiberg-Witten spectral curves. S-duality properties of the Calogero-Moser parameterization and conjectures on the Seiberg-Witten spectral curves ge...

The exchange operator formalism previously introduced for the Calogero problem is extended to the three-body Calogero-Marchioro-Wolfes one. In the absence of oscillator potential, the Hamiltonian of the latter is interpreted as a free particle Hamiltonian, expressed in terms of generalized momenta. In the presence of oscillator potential, it is regarded as a free modified boson Hamiltonian. The...

We prove that Calogero–Moser cells coincide with Kazhdan–Lusztig for dihedral groups in the equal parameter case.

First known examples of quasi-exactly-solvable N -body problems on the line are presented. These are related to the hidden algebra slN , and they are of two types – containing up to N and up to 6 body interactions only. Both types degenerate to the Calogero model. E-mail: [email protected] E-mail: [email protected] On leave of absence from the Institute for Theoretical and E...

We introduce and solve a generalized 1+1D Lorentzian gravity model in which a certain subclass of baby-universes is allowed, the occurrence of these being governed by a coupling constant β. Combining transfer matrix-, saddle pointand path integral techniques we show that for β < 1 it is possible to take a continuum limit in which the model is described by a 1D quantum Calogero Hamiltonian. The ...

We study the natural GL2-action on the Hilbert scheme of points in the plane, resp. SL2-action on the Calogero-Moser space. We describe the closure of the GL2-orbit, resp. SL2-orbit, of each point fixed by the corresponding diagonal torus. We also find the character of the representation of the group GL2 in the fiber of the Procesi bundle, and its Calogero-Moser analogue, over the SL2-fixed point.

It is shown that from some solutions of generalized Knizhnik-Zamolodchikov equations one can construct eigenfunctions of the Calogero-Sutherland-Moser Hamiltonians with exchange terms, which are characterized by any given permutational symmetry under particle exchange. This generalizes some results previously derived by Matsuo and Cherednik for the ordinary Calogero-Sutherland-Moser Hamiltonians.

Using a similarity transformation that maps the Calogero model into N decoupled quantum harmonic oscillators, we construct a set of mutually commuting conserved operators of the model and their simultaneous eigenfunctions. The simultaneous eigenfunction is a deformation of the symmetrized number state (bosonic state) and forms an orthogonal basis of the Hilbert (Fock) space of the model. This o...

Calogero-Moser systems are classical and quantum integrable multi-particle dynamics defined for any root system ∆. The quantum Calogero systems having 1/q2 potential and a confining q2 potential and the Sutherland systems with 1/ sin q potentials have “integer” energy spectra characterised by the root system ∆. Various quantities of the corresponding classical systems, e.g. minimum energy, freq...